Traveling around Abidjan requires certain precautions that you need to follow to ensure a safe stay. It is a good idea to look up the "Country Advice" on your Embassy's website (or that of the USA or UK or France) before travelling.

In the city, you can take taxis, they can be quite cheap but make sure that the meter works before boarding the taxi. There are two types of taxi, the orange one, with a meter, although you can negociate a fixed flat rate fare, or the "Woro Woro", communal taxies, colour various according to the district.  Fixed, cheap, flat rate fares, but only for the experienced visitor to Abidjan. The city operates buses but they are not quite safe. Best to take the "Express" which is a flat rate fare of 500 F CFA; these are seated only, no standing, and very safe.  Look up SOTRAs website for details of routes and frequency. If you are moving around in one just one neighbourhood, you can easily walk to the museums, markets or other places of interest, though not advisable at night.

Driving around shouldn't be a problem if you travel in a group. If driving outside Abidjan beware that roads are not in perfect condition and they are poorly lit at night. Accidents are frequent so take extra care and drive with a clear mind. Take your passport: there are military checkpoints where you will be asked to show the documents that you used when entering the country. Don't panic: they won't hassle you. Take a cell phone with you as on the road communications are scarce if non-existant.

Most large hotels offer a car hire service, almost excusively with a chauffeur. 

The train takes travelers to Ougadougou but it is not recommended as it traverses a conflictive region. There is a bus that takes you to Accra. It runs daily, and is air conditioned.

Since last editting this review in April, 2013, there have been a couple of "new arrivals" on the "Getting about Abidjan" scene, in the form of Private Hire Cabs, similar to Uber & Addison Lee in London, or LeCab in Paris.  These are "Taxijet" and "Africab", the latter using the same technology as the companies in London & Paris.  Details can be found on the Internet.  The latter have cars that are brand new, air-conditioned, uniformed and specially trained drivers, monitored by a central control room, uses GPS navigation

Also, the third bridge, a toll bridge, the Pont Henri Konan Bedie, has been opened, cutting dramatically the transit time from the airport to anyone travelling to Cocody, Riviera, Deux Plateau.  The toll is a mere 500 CFA ($0.8, 0.72€ or £0.58).